ENGLEWOOD, Colo. — The 347-word statement came down like a hammer only hours after Beth Bowlen announced her desire to be appointed controlling owner of the Denver Broncos.

The three trustees of The Patrick D. Bowlen Trust — Broncos president/CEO Joe Ellis, team counsel Rich Slivka and Denver attorney Mary Kelly — responded with a full-page retort stating the team’s longtime owner made it clear his children would not be entitled to a job with the organization, but rather have to earn a position of leadership.

Beth Bowlen, the trustees said, “is not capable or qualified at this time” after spending more than three years with the Broncos as their director of special projects and after receiving her law degree from the University of Denver’s Sturm College of Law.

“We have communicated our decision to Beth and her lawyers on multiple occasions,” the trustees wrote. “She is also fully informed as to why her employment with the team ended in...